(CNN) -- Diplomacy and coalition building. Individuals working for the whole. President Obama on Tuesday stressed that's how the United States prefers to solve some of the world's most complicated issues, particularly those in the Arab world.

Speaking at the United Nations General Assembly, and then at a Clinton Global Initiative event in New York, Obama repeatedly tried to drive home the value of conversation rather than force.

Tuesday began with Iran saying it had fired missiles into the Persian Gulf. Within hours of that claim, Obama took the podium at the annual gathering of U.N. member nations and discussed the threat of Iran obtaining a nuclear weapon.

"Let me be clear," the president said. "America wants to resolve this issue through diplomacy, and we believe that there is still time and space to do so.

"But that time is not unlimited."

A nuclear-armed Iran "is not a challenge that can be contained," he said, adding that the scenario would "threaten the elimination of Israel, the security of Gulf nations and the stability of the global economy," and trigger "a nuclear arms race in the region."

The U.S. "will do what we must to prevent Iran from obtaining a nuclear weapon," Obama added, without saying specifically what that meant.

Yet, echoing his 2008 campaign slogan, Obama told the General Assembly that he was "hopeful about the world we live in."

Obama also offered world leaders details about U.S. Ambassador Christopher Stevens, who was killed this month when a mob overtook the U.S. Embassy in Benghazi, Libya.

"Chris was born in a town called Grass Valley, California, the son of a lawyer and a musician," he began his speech. Stevens joined the Peace Corps and taught English in Morocco. He loved the people of North Africa and the Middle East, and spent his life trying to improve their lives.

Stevens was like so many foreign service workers who make tremendous personal sacrifices because they're passionate about building "bridges across oceans and cultures," Obama said.

"I tell you this story because Chris Stevens embodied the best of America." That means that the attacks in Benghazi, which also killed three other Americans, "were attacks on America."

The violence was "an assault on the very ideals upon which the United Nations was founded," he added.

Once again, Obama mentioned diplomacy, saying the attacks offended "the notion that people can resolve their differences peacefully; that diplomacy can take the place of war; and that in an interdependent world, all of us have a stake in working towards greater opportunity and security for our citizens."

He said he wanted more conversation about "the deeper causes of this crisis."

Adding more guards at embassies around the world isn't a solution, and neither is banning an anti-Muslim film that incited the chaos.

The way forward, the president said, is to make sure everyone understands that America represents the freedom to say anything and express views that some might find distasteful or offensive.

"As president of our country, I accept that people are going to call me awful things every day," he said. "And I will always defend their right to do so. Americans have fought and died around the globe to protect the right of all people to express their views -- even views that we disagree with."

The future should be determined by people like Stevens and not by his killers, Obama said.

The best way to do that, he said, must be international coalition building. Obama tried to drive that home not only at the U.N. but at an afternoon Clinton Global Initiative event, also in New York, where he spoke about ending human trafficking.

Earlier, he had signed an executive order to stem the crime, which he said victimizes more than 20 million people worldwide.

"Human trafficking ... must be called by its true name: modern slavery," Obama said.

The order makes it possible to provide more tools and training to federal prosecutors, law enforcement, immigration judges and transportation officials, among others, to identify and assist trafficking victims.

A $6 million awards challenge, supported by Goldman Sachs, to local communities to develop solutions to curb trafficking is also part of the order. There will also be several groups trying to formally measure and track human trafficking in the United States so that money can be precisely allocated to combat it.

Obama said human trafficking "distorts markets" and "endangers public health and fuels violence," he said.

"This is a no-brainer," the president said. "This is something we should all agree on," whether one is a Republican or Democrat.

Obama spoke directly to trafficked people.

"In the darkest hours of your lives, you may have felt utterly alone," he said.

"Our message to them: We see you."

That statement echoed a theme running through Obama's United Nations speech: hope.

Despite all of the world's tragedies and wars and struggle, Obama told U.N. members, he's optimistic.

"I am hopeful about the world we live in," he said.

He listed a string of reasons.

The Iraq war is over. Troops have returned home.

He noted that the U.S. continues to hand over control to locals in Afghanistan, and will bring all troops home in 2014.

"Al Qaeda has been weakened and Osama bin Laden is no more," Obama said.

Some people have praised the Obama administration's drone strikes that have killed terrorists, though the program remains highly controversial. And the Navy SEAL operation that resulted in the death of the 9/11 mastermind represents a major victory during Obama's tenure.

The president reminded listeners that it's been less than two years since a vendor in Tunisia set himself on fire to protest government corruption, triggering the so-called Arab Spring.

"I've seen hard choices made ... to put more power in the hands of citizens," he said, pointing out that the U.S. has supported transitions toward more open societies in the Arab world.

Yet a war still rages in one Arab nation. In the past year and a half, 26,000 people have died in Syria, according to groups fighting to oust President Bashar al-Assad.

Al-Assad's regime has been accused of torturing children, shooting unarmed protesters and going door to door in some villages, killing whole families. Al-Assad says that terrorists are behind the deaths.

The regime "must come to an end, so that the suffering of the Syrian people can stop," the president said, "and a new dawn can begin."

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